Classical Ciphers

Classical ciphers are the historical encryption techniques that laid the groundwork for modern cryptography. While they are no longer secure by today's standards, understanding them is essential for grasping the principles that underpin modern algorithms.

---

Substitution Ciphers

Substitution ciphers replace each letter in the plaintext with another letter or symbol.

Caesar Cipher

The Caesar cipher is one of the oldest known encryption techniques, used by Julius Caesar around 50 BC:

• Each letter is shifted by a fixed number of positions in the alphabet
• With a shift of 3: A becomes D, B becomes E, C becomes F, and so on

Plaintext:  HELLO WORLD
Shift:      3
Ciphertext: KHOOR ZRUOG

Why it is insecure:

• Only 25 possible shifts — all can be tried in seconds (brute force)
• The key space is far too small

ROT13

ROT13 is a special case of the Caesar cipher with a shift of 13:

A ↔ N    B ↔ O    C ↔ P    ...    M ↔ Z

Applying ROT13 twice returns the original text. It is used for trivial obfuscation (e.g., hiding spoilers) but provides zero security.

Monoalphabetic Substitution Cipher

A more general substitution cipher where each letter maps to a unique different letter:

Plaintext:  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Ciphertext: Q W E R T Y U I O P A S D F G H J K L Z X C V B N M

Key space: 26! (factorial) ≈ 4 × 10^26 possible keys — far too many to brute force.

But still insecure: Vulnerable to frequency analysis.

---

Frequency Analysis

Frequency analysis is a cryptanalytic technique developed by the Arab polymath Al-Kindi around 800 AD:

• In English, certain letters appear more frequently (E, T, A, O, I, N, S, H, R)
• By analysing letter frequencies in the ciphertext, an attacker can deduce the substitution

Letter	English Frequency
E	~12.7%
T	~9.1%
A	~8.2%
O	~7.5%
I	~7.0%
N	~6.7%
S	~6.3%
H	~6.1%
R	~6.0%

Example: If "X" appears most frequently in the ciphertext, it likely maps to "E".

Frequency analysis broke monoalphabetic ciphers and drove the development of more complex encryption methods.

---

Polyalphabetic Ciphers

Polyalphabetic ciphers use multiple substitution alphabets to defeat frequency analysis.

Vigenère Cipher

Invented in the 16th century and considered "unbreakable" for nearly 300 years:

• Uses a keyword to determine the shift for each letter
• Each letter of the keyword specifies a different Caesar shift

Plaintext:  ATTACKATDAWN
Keyword:    LEMONLEMONLE
Shift:      L=11, E=4, M=12, O=14, N=13, ...
Ciphertext: LXFOPVEFRNHR

How it works:

1. Write the keyword repeatedly above the plaintext
2. For each position, use the keyword letter to determine the Caesar shift
3. A = shift 0, B = shift 1, ..., Z = shift 25

Breaking the Vigenère cipher:

• Kasiski examination (1863) — find repeated sequences in the ciphertext to determine keyword length
• Friedman test — use the index of coincidence to estimate keyword length
• Once the keyword length is known, each position can be solved as a separate Caesar cipher using frequency analysis

---

Transposition Ciphers

Transposition ciphers rearrange the positions of plaintext characters without changing them.

Rail Fence Cipher

Characters are written in a zigzag pattern across a number of "rails" and then read off row by row:

Plaintext: WE ARE DISCOVERED FLEE AT ONCE
Rails: 3